Question

please answer with solution
1.find an angle which is 1/2 its complement
2.find an angle which is twice its complement
3.two complementary angles have a difference of 18 degrees. find their measures.
4.two supplementary angles have a difference of 64degrees. find their measures.
5.find the measure of the larger of two supplementary angles if the measure of the larger is 4times the smaller.

Answer 1

1. let x be one angle the other be y

they are complements so

x + y = 90

it says one is 1/2 the other so let's say x = 1/2 y

\[\frac 12 y + y = 90\]
if you combine like terms...
\[\frac 12 y + \frac 22 y = 90\]
\[\implies \frac 32 y = 90\]
cross multiply...
\[\implies 3y = 180\]
divide both sides by 3...
\\[\implies y = 60\]
so the complement is 90 - 60 = 30

so the angles are 60 and 30

does that help?
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